Let's modify the logistic differential equation of this example as follows: OP -0.050 (1-1000)- (a) Suppose P(1) represents a fish population at time t, where t is measured in weeks. Explain the meaning of the final term in the equation (-12). The term -12 represents a harvesting of fish at a constant ✔rate-in this case, 12 [lish/week✔✔✔ This is the rate at which fish are caught (b) Draw a direction field for this differential equation. Use the direction field to sketch several solution curves. P 1200) E P 1000! ● 800 600k P = 450 400 200 of 0 P 1200 1000 800 600 12 1 400 ***L 50 100 150 200 250 300 350 For P600, P(t)-Select-- For Po> 600, P(t)-Select- v V V 1500 v 1000 Describe what happens to the fish population for various initial populations. For 0 < P < 400, P(t) -Select--- For P 400, P(t)-Select-- For 400 < P < 600, P(t)-Select-- O Graph the solutions and compare with your sketches in part (b). P 500 (c) What are the equilibrium solutions? (Enter your answers as a comma-separated list.) Pa 1300 044 flip 0 50 100 150 200 250 300 350 P 1000 ***** .. 500 (d) Solve this differential equation explicitly, either by using partial fractions or with a computer algebra system. Use the initial populations 350 and 4 P-350 " P